"Kahvaltıda domates yerim."

To quote from the Wikipedia article I linked above:

• Many English nouns can be used in either mass or count syntax, and in these cases, they take on cumulative reference when used as mass nouns. For example, one may say that "there's apple in this sauce," and then apple has cumulative reference, and, hence, is used as a mass noun. The names of animals, such as "chicken", "fox" or "lamb" are count when referring to the animals themselves, but are mass when referring to their meat, fur, or other substances produced by them. (e.g., "I'm cooking chicken tonight" or "This coat is made of fox.")
• Nouns differ in the extent to which they can be used flexibly, depending largely on their meanings and the context of use. For example, the count noun "house" is difficult to use as mass (though clearly possible), and the mass noun "cutlery" is most frequently used as mass, despite the fact that it denotes objects, and has count equivalents in other languages [...]

The examples include this gem: "You get a lot of house for your money since the recession."

This is absolutely straightforward, uncontroversial linguistics. It's just not linguistics that is usually stressed in the literature, because compared to certain other questions related to the distinction, experts consider this boring.

Native speaker judgements about grammaticality are notoriously unreliable. My own judgements about my native German generally tend to be a bit less reliable than my judgements about English. Sometimes I reject a construction as ungrammatical under all circumstances, and the next day I realise that in a very special context that I didn't think of it's perfectly fine and I have used it myself before.

And as I said before, it may depend on the speaker. One of the most obvious factors is varieties of English. I have never lived in the US, so I can't say much about language use there, but I have studied and worked a few years in England and I am sure the construction is fine there.

The distinction between count nouns and mass nouns in real English has always been statistical rather than strict. Good authors use mass nouns as count nouns and count nouns as mass nouns - when appropriate. Being able to eat and digest tomato is one of those contexts where it's better to use tomato as a mass noun - at least in British English, but probably also in American English. Eating tomato(es) for breakfast is a borderline case where it's fine either way.

Deriving a new mass noun from the homonymous count noun is a routine linguistic operation that every competent native speaker can do easily and will in fact do quite often both in casual speech and in formal writing. (In formal writing they may self-censor, however, due to misunderstandings about how language actually works.) In the previous post I have given you evidence for the fact that people do in fact do this with tomato and with apple (a word that is helpful here because it's more common).

Note that this is not the first time such a question has come up at Duolingo. The Spanish sentence Nuestro gato come huevo is officially translated as "Our cat eats egg." That's more dubious than what I am proposing here, though it makes sense when humorously treating the cat as a family member with particular dietary needs. (Google's n-gram viewer has examples of "eat apple" at the end of the sentence, but not of "eat tomato" or "eat egg" in the same position.)

Also, there was once an insightful discussion over at the linguistics blog separated by a common language. The author of the blog mis-categorised scrambled egg[s] and mashed potato[s] as universally mass nouns in British English because they can be used as such in the appropriate context. This was pointed out by British reader Harry Campbell:

• Actually, I don't think it's as simple as scrambled egg(BrE), scrambled eggs (AmE). I think there is a, sometimes subtle, distinction in BrE betwen the dish and the food seen as the substance that the dish is made of. One would still serve scrambled eggs, but if you spilled some on your shirt it would be scrambled egg you would scrape off. "My favourite food is mashed potatoes" but "that stuff has the consistency of mashed potato". To take a clearer case, one would of course serve baked potatoes or order a baked potato, but by the actual (uncountable) stuff that your baked potato is made of is baked potato. Would an American say "you've got scrambled eggs on your tie"? Would it be "you've got (mashed/baked/whatever) potato on your tie" or "potatoes"?

American reader lynneguist then confirmed that Americans make basically the same distinction:

• The ingredient-in-something else thing is a situation where a countable is likely to become a mass noun (as with the 'on your tie' situation). E.g. I would fill something with beet and onion, not beets and onions, if they had been rendered into some mashed/chopped form.
• Also, when it's being used as a modifier of something else, it'd naturally go to singular in AmE, as in 'mashed potato situation', 'mashed potato variations' 'mashed potato cake', etc. [...]

I really think this is such a specific example of pulp allergies and dated references... If I said to anyone I know "I eat tomato at/for breakfast" they would probably give me a strange look and think I'm talking funny. And the specific example you're citing isn't really /this/ one. If there's a context of dietary needs/restrictions, sure, OK. But this stand-alone sentence, it's probably going to be tomatoes or a tomato.

"meat," "fish," and "fruit" are all mass nouns. Most fruits and vegetables themselves are not though.

I can reassure you as a person who has been speaking English his entire life that "to eat tomato" only really works when you are talking about tomato flavored things. A good example would be with tortillas, which come in various flavors in the US, "There are so many flavors of tortillas at this restaurant. I don't each spinach ones but I do eat tomato," is fine. This construction normally only works nowadays with "x-flavored things."

Now as for the English language in the 1920s and the 19th century, I can say nothing about that. It does not reflect language today. I also checked with several people on this just to be sure...at least it was universal agreement among the gaggle of Americans that I have asked. :)